Complex manifolds with negative curvature operator
Differential Geometry
2019-04-01 v1 Complex Variables
Abstract
We prove that compact complex manifolds with admitting metrics with negative Chern curvature operator either admit a -exact positive (1,1) current, or are K\"ahler with ample canonical bundle. In the case of complex surfaces we obtain a complete classification. The proofs rely on a global existence and convergence result for the pluriclosed flow.
Cite
@article{arxiv.1903.12645,
title = {Complex manifolds with negative curvature operator},
author = {Man-Chun Lee and Jeffrey Streets},
journal= {arXiv preprint arXiv:1903.12645},
year = {2019}
}